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Amachine produces parts that are ej, i eith, slightly defective (2%), or obvious er good (90%),, , ly defective (8%),, Produced parts get passed through an stones, , inspection machine, which is able to det, 3 , ect an, that is obviously defective and discard it. What i, , the probability of the parts that make it through the, inspection machine and get shipped?, (a) 0.789 (b) 0.978, (c) 0.542 (d) 0.234, , P has 2 children. He has a son, Jatin. What is the, probability that Jatin's sibling is a brother?, , yl bp) 4 2 l, (a ; ) 2 3 @) 5, , If A and B are 2 events such that P(A) > 0 and, P(B) #1, then P(A|B)=, , (a) 1-P(A|B) (b) 1-P(A|B), 1- P(AUB) P(A), (c) 3B) @® 5B), , Consider the game of ‘Let's Make a Deal’ in, which there are three doors (numbered 1, 2, 3),, one of which has a car behind it and two of, which are empty (have "booby prizes"). You, initially select Door 1, then, before it is opened,, Monty Hall tells you that Door 3 is empty |, (has a booby prize), You are then given the option to, switch your selection from Door 1 to the unopened, Door 2. What is the probability that you will win the |, car if you switch your door selection to Door 2?, 1 1, (a) : (b) 4, 1 (d) None of these, , (c), If two events A and B are such that P(A)= 0.3,, P(B)=0.4and P(AAB)=0.5 then P(B|(AUB))=, , 1 1 2 @t, @) 5 (b) : (c) : @:, , Nm

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If E and F are events such that 0 < P(F) < 1, then, (a) P(E|F)+P(E|F)=1, , (b) P(E|F)+P(E|F)=1, , (c) P(E|F)+P(E|F)=1, , (d) P(E|F)+P(E|F)=0, , A die is thrown three times. Events A and B are, , defined as below:, A:'40n the third throw’ and B : '6 on the first and, 5 on the second throw’. Find the probability of A, given that B has already occurred., , 2 l 1 2, , (a) 3 (b) é (c) 7 (d) 7, , Suppose that five good fuses and two defective ones, have been mixed up. To find the defective fuses,, we test them one-by-one, at random and without, replacement. What is the probability that we are, lucky and find both of the defective fuses in the first, two tests?, , @+ 062 @1 @t, , 42 21 18 21, , If six cards are selected at random (without, replacement) from a standard deck of 52 cards, what, is the probability that there will be no pairs? (two, cards of same denomination), , (a) 0.28 (b) 0.562, , (c) 0.345 (d) 0.832, P(E 7 F) is equal to, , (a) P(E)-P(FIE) (b) P(F)-P(E|F), , (c) Both (a)and(b) — (d) None of these, , An urn contains 10 black and 5 white balls. ‘Two, balls are drawn from the urn one after the other, without replacement, then the probability that both, drawn balls are black, is, , 2 1 5 3, . = Ed d) =, (a) ; (b) ; (c) ; (d) :

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13., , 13., , 14., , 15., , If three events of a sample space are E, F and G, then, P(E FOG) is equal to, , (a) P(E) P(FIE) P(G\(EO F)), , (b) P(E) P(FIE) P(GIEF)), , (c) Both (a) and (b), , (d) None of these, , Three cards are drawn successively, without :, replacement from a pack of 52 well shuffled cards, |, then the probability that first two cards are kings, , and the third card drawn is an ace, is, 2 1 2 1, oiemcminas ——— — d ———, () 5525 ©) 5525 (c) 5527 (¢) 5527, A bag contains 12 white pearls and 18 black, pearls. Two pearls are drawn in succession without, replacement. Find the probability that the first pearl, is white and the second is black., 32 28 36 36, a) — b) 2 c) — (d —, (a) 145 143 : 145 143, Two cards are drawn at random one by one without, replacement from a pack of 52 playing cards. Find, , the probability that both the cards are black., , 21 2 23 25, — () 2 = tay =, (a) 17 (b) 702 (c) ie (d) md

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16. Abag contains 20 tickets, numbered 1 to 20. A ticket, , 17., , 18., , 19., , is drawn and then another ticket is drawn without :, replacement. Find the probability that both tickets |, , will show even numbers., , 9 q 16 7 aw, (a) 3 (b) Pes (c) a (d) 30, , A bag contains 6 red, 5 blue and 7 white balls. Ifthree, balls are drawn one by one (without replacement), —, then what is the probability that all three balls are —, blue? 3, @ 2 wo 2 @ 3 ws, , 204 408 204 408, Two balls are drawn one after another (without, replacement) from a bag containing 2 white, 3 red, and 5 blue balls. What is the probability that atleast, one ball is red?, , 7 8 7 5, J, a _ d) =, (a) 5 (b) 5 (c) 16 (d) 16, A box contains 2 black, 4 white and 3 red balls., One ball is drawn at random from the box and kept, aside, From the remaining balls in the box, another, ball is drawn at random and kept beside the first., The process is repeated, find the probability that the, balls drawn are in the sequence of 2 black, 4 white, and 3 red. 3 3, 1, 9 (ce) —— (d), @) 560 © ine i360 i360

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20. Two cards are drawn successively from a well, , | 21., , | 22., , 23., , shuffled pack of 52 cards. Find the probability that, , one is a red card and the other is a queen., 103 101 101 103, — () — t&) — @d) —, @) i326 © i326 1426 1426, , For any two events A and B,, P(A)+P(B)+1, (a) P(A|B)2 P(B), (b) P(AQ B)=P(A)—P(AMB) does not hold, (c) P(AU B)=1-P(A)-P(B), if A and B are, independent, (d) P(AU B)=1—P(A)-P(B) if A and B are, dependent, Let A and B be independent events with P(A) = 1/4, and P(A U B) = 2P(B) - P(A). Find P(B), ares ee a, 4 5 3 5, Let three fair coins be tossed. Let A = {all heads or all, tails}, B = {atleast two heads}, and C = {atmost two, tails}. Which of the following events are independent ?, (a) AandC (b) BandC, (c) AandB (d) None of these, , Two events A and B will be independent, if, (a) Aand Bare mutually exclusive, , (b) P(A’ B’) = [1 ~ P(A) [1 - P(B)], , (c) P(A) = P(B), , (d) P(A) + P(B) =1